This recipe is brought to us by Zarela Martinez, owner and chef at Zarela restaurant in New York City.
Combine pork, the unpeeled onion and unpeeled garlic, 1 teaspoon salt, and 1/2 teaspoon peppercorns in a medium stockpot. Add water to cover by about 1 inch. Cover and bring to a boil, immediately reduce heat to maintain a slow rolling boil, skimming off any froth that rises to the surface. Cook, partially covered, until the meat is tender, about 45 minutes. Transfer meat to a bowl, letting it drain well; reserve the liquid, and set the meat aside. Strain the liquid through a fine-mesh sieve; there should be 3 to 4 cups. Wipe out the pot, and return stock to pot; set aside.
Cut pumpkin or squash into 8 equal chunks, removing any seeds or strings. Add to stock and bring to a boil. Reduce heat to maintain a low rolling boil and cook until tender, about 30 minutes. Remove pumpkin, and drain well in a colander. Cool to room temperature. Reserve stock for another use. Scrape pumpkin flesh into a bowl, discarding the skin. Mash the flesh thoroughly; set aside.
Meanwhile; bring 2 to 3 cups water to a boil in a small saucepan. Add the dried chiles, and cook, uncovered, until softened, about 5 minutes. Drain, stem and seed the chiles; set aside.
Place pumpkin seeds in a small skillet over medium-low heat. Toast, stirring and shaking skillet, until the seeds begin to swell and pop, 3 to 5 minutes; set aside. In a spice grinder or a mortar and pestle, combine the cumin, coriander, and remaining 1/2 teaspoon peppercorns. Grind until fine; set aside.
In the jar of a blender, combine the coarsely chopped onion, finely chopped garlic, tomatoes, drained chiles, pumpkin seeds, and ground spices; puree until smooth.
In a medium saucepan, heat 2 tablespoons lard over medium-high heat until rippling. Add the pureed tomato mixture. Reduce heat to medium, cover, and cook, stirring occasionally, until the fat starts to separate, about 15 minutes. Add the reserved mashed pumpkin or squash and the vinegar, stirring to mix well. Cook, covered, for 10 minutes more. Taste and adjust for seasoning.
Heat the remaining 2 tablespoons lard in a large skillet over medium-high heat. Add the pork, seasoning with salt and pepper. Cook until lightly browned and crisp, but not dry, about 5 minutes.
Spoon seasoned pumpkin or squash mixture onto a platter and top with pork.